H2O + Cl2 + I2 = HCl + HIO3

H_2O (water) + Cl_2 (chlorine) + I_2 (iodine) ⟶ HCl (hydrogen chloride) + HIO_3 (iodic acid)

Balance the chemical equation algebraically: H_2O + Cl_2 + I_2 ⟶ HCl + HIO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cl_2 + c_3 I_2 ⟶ c_4 HCl + c_5 HIO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl and I: H: | 2 c_1 = c_4 + c_5 O: | c_1 = 3 c_5 Cl: | 2 c_2 = c_4 I: | 2 c_3 = c_5 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 5 c_3 = 1 c_4 = 10 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 5 Cl_2 + I_2 ⟶ 10 HCl + 2 HIO_3

+ + ⟶ +

water + chlorine + iodine ⟶ hydrogen chloride + iodic acid

| water | chlorine | iodine | hydrogen chloride | iodic acid molecular enthalpy | -285.8 kJ/mol | 0 kJ/mol | 0 kJ/mol | -92.3 kJ/mol | -230.1 kJ/mol total enthalpy | -1715 kJ/mol | 0 kJ/mol | 0 kJ/mol | -923 kJ/mol | -460.2 kJ/mol | H_initial = -1715 kJ/mol | | | H_final = -1383 kJ/mol | ΔH_rxn^0 | -1383 kJ/mol - -1715 kJ/mol = 331.8 kJ/mol (endothermic) | | | |

Construct the equilibrium constant, K, expression for: H_2O + Cl_2 + I_2 ⟶ HCl + HIO_3 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 6 H_2O + 5 Cl_2 + I_2 ⟶ 10 HCl + 2 HIO_3 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2O | 6 | -6 Cl_2 | 5 | -5 I_2 | 1 | -1 HCl | 10 | 10 HIO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) Cl_2 | 5 | -5 | ([Cl2])^(-5) I_2 | 1 | -1 | ([I2])^(-1) HCl | 10 | 10 | ([HCl])^10 HIO_3 | 2 | 2 | ([HIO3])^2 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([H2O])^(-6) ([Cl2])^(-5) ([I2])^(-1) ([HCl])^10 ([HIO3])^2 = (([HCl])^10 ([HIO3])^2)/(([H2O])^6 ([Cl2])^5 [I2])

Construct the rate of reaction expression for: H_2O + Cl_2 + I_2 ⟶ HCl + HIO_3 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 6 H_2O + 5 Cl_2 + I_2 ⟶ 10 HCl + 2 HIO_3 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2O | 6 | -6 Cl_2 | 5 | -5 I_2 | 1 | -1 HCl | 10 | 10 HIO_3 | 2 | 2 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term H_2O | 6 | -6 | -1/6 (Δ[H2O])/(Δt) Cl_2 | 5 | -5 | -1/5 (Δ[Cl2])/(Δt) I_2 | 1 | -1 | -(Δ[I2])/(Δt) HCl | 10 | 10 | 1/10 (Δ[HCl])/(Δt) HIO_3 | 2 | 2 | 1/2 (Δ[HIO3])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/6 (Δ[H2O])/(Δt) = -1/5 (Δ[Cl2])/(Δt) = -(Δ[I2])/(Δt) = 1/10 (Δ[HCl])/(Δt) = 1/2 (Δ[HIO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | chlorine | iodine | hydrogen chloride | iodic acid formula | H_2O | Cl_2 | I_2 | HCl | HIO_3 Hill formula | H_2O | Cl_2 | I_2 | ClH | HIO_3 name | water | chlorine | iodine | hydrogen chloride | iodic acid IUPAC name | water | molecular chlorine | molecular iodine | hydrogen chloride | iodic acid

| water | chlorine | iodine | hydrogen chloride | iodic acid molar mass | 18.015 g/mol | 70.9 g/mol | 253.80894 g/mol | 36.46 g/mol | 175.91 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 0 °C | -101 °C | 113 °C | -114.17 °C | 110 °C boiling point | 99.9839 °C | -34 °C | 184 °C | -85 °C | density | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | 4.94 g/cm^3 | 0.00149 g/cm^3 (at 25 °C) | 4.629 g/cm^3 solubility in water | | | | miscible | very soluble surface tension | 0.0728 N/m | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 0.00227 Pa s (at 116 °C) | | odor | odorless | | | |